 CGAL 4.12 - Polynomial
PolynomialTraits_d::SquareFreeFactorize Concept Reference

## Definition

This Functor computes a square-free factorization of a PolynomialTraits_d::Polynomial_d.

A polynomial $$p$$ is factored into square-free and pairwise coprime non-constant factors $$g_i$$ with multiplicities $$m_i$$ and a constant factor $$a$$, such that $$p = a \cdot g_1^{m_1} \cdot ... \cdot g_n^{m_n}$$.

The pairs $$(g_i,m_i)$$ are written into the given output iterator.

This functor is well defined if PolynomialTraits_d::Polynomial_d is a UniqueFactorizationDomain.

Refines:

DefaultConstructible

Polynomial_d
PolynomialTraits_d
PolynomialTraits_d::SquareFreeFactorizeUpToConstantFactor
PolynomialTraits_d::MakeSquareFree
PolynomialTraits_d::IsSquareFree

## Operations

template<class OutputIterator >
OutputIterator operator() (PolynomialTraits_d::Polynomial_d p, OutputIterator it, PolynomialTraits_d::Innermost_coefficient_type &a)
Computes the square-free factorization of $$p$$ and returns the past-the-end iterator of the written range. More...

template<class OutputIterator >
OutputIterator operator() (PolynomialTraits_d::Polynomial_d p, OutputIterator it)
As the first operator, just not computing the factor $$a$$.

## ◆ operator()()

template<class OutputIterator >
 OutputIterator PolynomialTraits_d::SquareFreeFactorize::operator() ( PolynomialTraits_d::Polynomial_d p, OutputIterator it, PolynomialTraits_d::Innermost_coefficient_type & a )

Computes the square-free factorization of $$p$$ and returns the past-the-end iterator of the written range.

Precondition
std::iterator_traits< OutputIterator >::value_type must be constructible from std::pair<PolynomialTraits_d::Polynomial_d,int>.